Problem 3E

Let P(n) be the statement that a postage of ncentscanbe formed using just 3-cent stamps and 5-cent stamps The parts of this exercise outline a strong induction proof that P(n) is true for n ≥ 8.

a) Show that the statements P(8), P(9), and P(10) are true, completing the basis step of the proof.

b) What is the inductive hypothesis of the proof?

c) What do you need to prove in the inductive step?

d) Complete the inductive step for k ≥ 10.

e) Explain why these steps show that this statement is true whenever n ≥ 8.

Discrete Mathematics CS225 Terms and concepts: Week 2 Reading 145-159, 165-167. 183-184. 201-203 and Lectures and Supplemental Info List of Types of Numbers: • Natural numbers ( ℕ ): Counting numbers. {0, 1, 2, 3…} • Integers ( ℤ ): Positive and negative counting numbers. {…-2, -1, 0, 1, 2, …} • Rational numbers ( ℚ ): Numbers that can be expressed as a ratio of an integer to a non-zero integer. ◦ Quotients of integers. ◦ All integers are rational, but not all rational numbers are integers. • Real numbers ( ℝ ) : Numbers that have decimal representations. ◦ Can be positive, negative, or zero. ◦ All rational numbers are real, not all real numbers are rational. • Irrational numbers (I): Real numbers that are not rationa